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Journal of Control Science and Engineering
Volume 2007 (2007), Article ID 27190, 8 pages
Research Article

Sensitivity Limitations for Multivariable Linear Filtering

School of Electrical Engineering and Computer Science, The University of Newcastle, Callaghan 2308, NSW, Australia

Received 14 August 2006; Accepted 22 August 2007

Academic Editor: Shinji Hara

Copyright © 2007 Steven R. Weller. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper examines fundamental limitations in performance which apply to linear filtering problems associated with multivariable systems having as many inputs as outputs. The results of this paper quantify unavoidable limitations in the sensitivity of state estimates to process and measurement disturbances, as represented by the maximum singular values of the relevant transfer matrices. These limitations result from interpolation constraints imposed by open right half-plane poles and zeros in the transfer matrices linking process noise and output noise with state estimates. Using the Poisson integral inequality, this paper shows how sensitivity limitations and tradeoffs in multivariable filtering problems are intimately related to the directionality properties of the open right half-plane poles and zeros in these transfer matrices.